Finite Group Databasebeta

← Q8×(C22⋊D59)⋊C4 #28748548

Subgroups — Q8×(C22⋊D59)⋊C4 #28748548

Order 15104.

3148 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C22⋊D59C211yesmaximal, characteristic
2C22×Q8×Dic59C211yesmaximal, characteristic, complemented
3C2×C4×Q8×D59C211yesmaximal, characteristic, complemented
4#21427153C213yesmaximal, complemented
5#21427106C213yesmaximal, complemented
6#21427099C213yesmaximal, complemented
7Q8×Dic59⋊C4C211yesmaximal, characteristic, complemented
8#21426992C213yesmaximal
9Q8×(C2×D59)⋊C4C211yesmaximal, characteristic, complemented
10#21426665C213yesmaximal, complemented
11#21426634C213yesmaximal, complemented
12#21426624C213yesmaximal, complemented
13C4×Q8×Dic59C211yesmaximal, characteristic, complemented
14C4×(C22⋊D59)⋊C4C213yesmaximal
15Q8×C22⋊C4×C59C211yesmaximal, characteristic, complemented
16C22×Q8×D59C2211yescharacteristic
17Q8×C22⋊D59C4116yescomplemented
18C2×#14273725C2213yes—
19C2×#14273706C2213yes—
20C2×#14273703C2213yes—
21C2×Q8×Dic59—28no—
22C2×Q8×Dic59C2211yescharacteristic
23C2×Q8×Dic59C2213yes—
24C2×Q8×Dic59C2213yes—
25C2×Q8×Dic59C2211yescharacteristic
26C2×Q8×Dic59C2211yescharacteristic
27C2×C4×Dic118C2213yes—
28C2×#14273692C2213yes—
29C4×Q8×D59—28no—
30C2×C4×C22⋊D59C2213yes—
31C2×(C22⋊D59)⋊C4C2213yes—
32C2×(C22⋊D59)⋊C4C2211yescharacteristic
33C22×C4⋊Dic59C2213yes—
34C2×C4⋊C4×D59C2213yes—
35C22×C4×Dic59C2213yes—
36C2×C42×D59C2213yes—
37#16837308C2213yes—
38#16837307C2213yes—
39#16837300C2213yes—
40#16837299C2216yes—
41#16837299C2216yes—
42#16837298C2213yes—
43#16837289C2216yes—
44#16837284C2216yes—
45#16837276C2216yes—
46#16837274C2216yes—
47#16837271C2213yes—
48#16837259C2213yes—
49C4⋊C4×Dic59C2213yes—
50C4⋊C4×Dic59C2213yes—
51C4×Dic59⋊C4C2213yes—
52C4×C4⋊Dic59C2213yes—
53#16837253C2213yes—
54#16837253C2213yes—
55#16837253C2216yes—
56C22⋊C4×Dic59C2213yes—
57C22⋊C4×Dic59C2213yes—
58C4×(C2×D59)⋊C4C2213yes—
59#16837249C2213yes—
60#16837249C2213yes—
61C42×Dic59C2213yes—
62C23×Q8×C59C2211yescharacteristic
63C2×C4×Q8×C59C2211yescharacteristic
64C2×C4×Q8×C59C2211yescharacteristic
65C59×#391C2213yes—
66C59×#391C2213yes—
67C59×#380C2213yes—
68C4×C22⋊C4×C59C2213yes—
69C22×Dic118C2313yes—
70C2×Q8×D59—24no—
71C2×Q8×D59—24no—
72C2×Q8×D59C2×C418yescomplemented
73C22×C22⋊D59C2311yescharacteristic
74C23×Dic59C2313yes—
75C23×Dic59C2311yescharacteristic
76C22×C4×D59C2313yes—
77C22×C4×D59C2313yes—
78C22×C4×D59C2311yescharacteristic
79#14273725C2×C4124yescomplemented
80#14273706C2×C4124yescomplemented
81#14273703C2×C4124yescomplemented
82Q8×Dic59—24no—
83Q8×Dic59—212no—
84Q8×Dic59—212no—
85Q8×Dic59C2×C418yescomplemented
86Q8×Dic59D418yescomplemented
87C4×Dic118—212no—
88#14273692—212no—
89C4×C22⋊D59C2×C4124yes—
90(C22⋊D59)⋊C4—212no—
91(C22⋊D59)⋊C4Q818yesdirect product factor
92C2×C4⋊Dic59—212no—
93C2×C4⋊Dic59C2313yes—
94C2×C4⋊Dic59C2316yes—
95C2×C4⋊Dic59C2313yes—
96C2×C4⋊Dic59C2313yes—
97C2×Dic59⋊C4C2313yes—
98C2×Dic59⋊C4C2316yes—
99C2×Dic59⋊C4C2316yes—
100C2×Dic59⋊C4C2316yes—
101C2×Dic59⋊C4C2313yes—
102C2×Dic59⋊C4C2311yescharacteristic
103C4⋊C4×D59—212no—
104C2×C22⋊Dic59C2313yes—
105C2×(C2×D59)⋊C4C2313yes—
106C2×(C2×D59)⋊C4C2313yes—
107C2×(C2×D59)⋊C4C2311yescharacteristic
108C2×C4×Dic59—212no—
109C2×C4×Dic59C2313yes—
110C2×C4×Dic59C2313yes—
111C2×C4×Dic59C2313yes—
112C2×C4×Dic59C2313yes—
113C2×C4×Dic59C2313yes—
114C2×C4×Dic59C2313yes—
115C2×C4×Dic59C2313yes—
116C2×C4×Dic59C2313yes—
117C2×C4×Dic59C2313yes—
118C2×C4×Dic59C2313yes—
119C2×C4×Dic59C2311yescharacteristic
120C42×D59—212no—
121C59⋊#95C2313yes—
122C59⋊#95C2313yes—
123C59⋊#95C2313yes—
124C59⋊#95C2313yes—
125C59⋊#95C2316yes—
126C59⋊#95C2316yes—
127C22×Q8×C59—24no—
128C22×Q8×C59—24no—
129C22×Q8×C59C2×C418yescomplemented
130C22×Q8×C59C2313yes—
131C22×Q8×C59C2311yescharacteristic
132C23×C4×C59C2313yes—
133C4×Q8×C59—24no—
134C4×Q8×C59—24no—
135C2×C4⋊C4×C59C2313yes—
136C2×C4⋊C4×C59C2313yes—
137C2×C22⋊C4×C59C2313yes—
138C2×C22⋊C4×C59C2311yescharacteristic
139C2×C42×C59C2313yes—
140C2×C42×C59C2313yes—
141#95×C59C2313yes—
142#95×C59C2313yes—
143#95×C59C2316yes—
144C24×C59C2411yescharacteristic
145C23×D59C2411yescharacteristic
146C2×Q8×C59—232no—
147C2×Q8×C59—26no—
148C2×Q8×C59—26no—
149C2×Q8×C59C22×C4112yes—
150C2×Q8×C59C22×C414yes—
151C2×Q8×C59C2×D414yes—
152C2×Q8×C59#4114yes—
153C22×C4×C59—26no—
154C22×C4×C59—26no—
155C22×C4×C59C22×C4112yes—
156C22×C4×C59C2413yes—
157C22×C4×C59C2413yes—
158C22×C4×C59C2413yes—
159C22×C4×C59C2411yescharacteristic
160C22×C4×C59C2411yescharacteristic
161C22×C4×C59C2413yes—
162C2×C22⋊D59C22×C414yes—
163C2×C22⋊D59C2×Q814yes—
164C2×C22⋊D59#4114yes—
165C22×Dic59—22no—
166C22×Dic59—22no—
167C22×Dic59—26no—
168C22×Dic59—26no—
169C22×Dic59—43no—
170C22×Dic59C2×Q814yescomplemented
171C22×Dic59C2413yes—
172C22×Dic59C2413yes—
173C22×Dic59C2413yes—
174C22×Dic59C2413yes—
175C22×Dic59C2411yescharacteristic
176C22×Dic59C2411yescharacteristic
177C22×Dic59C2411yescharacteristic
178Q8×D59—232no—
179C2×C4×D59—26no—
180C2×C4×D59—26no—
181C2×C4×D59—22no—
182C2×C4×D59—22no—
183C2×C4×D59—26no—
184C2×C4×D59—26no—
185C2×C4×D59—43no—
186C2×C4×D59C22×C4112yes—
187C2×C4×D59C2×Q814yescomplemented
188C2×Dic118—26no—
189C2×Dic118—26no—
190C2×Dic118C22×C4112yes—
191C4⋊C4×C59—26no—
192C4⋊C4×C59—26no—
193C22⋊C4×C59—26no—
194C22⋊C4×C59C2×Q814yescomplemented
195C42×C59—26no—
196C42×C59—26no—
197C22⋊Dic59C22×C4112yes—
198(C2×D59)⋊C4—26no—
199(C2×D59)⋊C4C22×C4112yes—
200(C2×D59)⋊C4C2×Q814yescomplemented
201C4⋊Dic59—26no—
202C4⋊Dic59—212no—
203C4⋊Dic59C22×C4112yes—
204C4⋊Dic59C2×D4112yes—
205Dic59⋊C4—212no—
206Dic59⋊C4—26no—
207Dic59⋊C4—46no—
208Dic59⋊C4C22×C4112yes—
209Dic59⋊C4C22×C4124yes—
210Dic59⋊C4C2×Q814yescomplemented
211C4×Dic59—26no—
212C4×Dic59—26no—
213C4×Dic59—26no—
214C4×Dic59—26no—
215C4×Dic59—26no—
216C4×Dic59—26no—
217C4×Dic59—26no—
218C4×Dic59—43no—
219C4×Dic59C22×C4112yes—
220C4×Dic59C2×D4112yes—
221C4×Dic59C2×Q814yescomplemented
222C23×C59—21no—
223C23×C59—21no—
224C23×C59—21no—
225C23×C59—21no—
226C23×C59C23×C412yes—
227C23×C59C22×Q812yes—
228C23×C59C2×#4112yes—
229C23×C59C2511yescharacteristic
230C22×D59—21no—
231C22×D59—21no—
232C22×D59—21no—
233C22×D59—21no—
234C22×D59C23×C412yes—
235C22×D59C22×Q812yes—
236C22×D59C2×#4112yes—
237Q8×C59—224no—
238Q8×C59C4×D4116yescomplemented
239C2×C4×C59—21no—
240C2×C4×C59—23no—
241C2×C4×C59—21no—
242C2×C4×C59—23no—
243C2×C4×C59—21no—
244C2×C4×C59—21no—
245C2×C4×C59—224no—
246C2×C4×C59—23no—
247C2×C4×C59—23no—
248C2×C4×C59—23no—
249C2×C4×C59—23no—
250C2×C4×C59—23no—
251C2×C4×C59—23no—
252C2×C4×C59C23×C416yes—
253C2×C4×C59C23×C416yes—
254C2×C4×C59C22×D416yes—
255C2×C4×C59C22×Q812yes—
256C2×C4×C59C22×Q812yes—
257C2×C4×C59C2×#4116yes—
258C22⋊D59C4×Q8116yescomplemented
259C2×Dic59—21no—
260C2×Dic59—23no—
261C2×Dic59—23no—
262C2×Dic59—23no—
263C2×Dic59—23no—
264C2×Dic59—21no—
265C2×Dic59—23no—
266C2×Dic59—23no—
267C2×Dic59—28no—
268C2×Dic59—23no—
269C2×Dic59—23no—
270C2×Dic59—23no—
271C2×Dic59—412no—
272C2×Dic59C23×C416yes—
273C2×Dic59C23×C416yes—
274C2×Dic59C23×C412yes—
275C2×Dic59C22×D416yes—
276C2×Dic59C22×D412yes—
277C2×Dic59C22×Q812yes—
278C2×Dic59C22×Q812yes—
279C2×Dic59C22×Q812yes—
280C2×Dic59C2×#4112yes—
281C2×Dic592−1+412yes—
282C4×D59—224no—
283C4×D59—28no—
284C4×D59—412no—
285Dic118—224no—
286C4×D4×Q8—591nomaximal, Sylow
287C22×C59—22no—
288C22×C59—22no—
289C22×C59—22no—
290C22×C59—22no—
291C22×C59—22no—
292C22×C59—22no—
293C22×C59C2×C4×Q814yescomplemented
294C22×C59C24×C411yescharacteristic
295C22×C59C23×D411yescharacteristic
296C22×C59C23×Q811yescharacteristic
297C22×C59C22×#4111yescharacteristic
298C22×C59C22×#4111yescharacteristic
299C22×C59C2×2−1+411yescharacteristic
300C22×C59#58511yescharacteristic
301C2×D59—22no—
302C2×D59—22no—
303C2×D59—22no—
304C2×D59—22no—
305C2×D59—22no—
306C2×D59—22no—
307C2×D59C2×C4×Q814yescomplemented
308C4×C59—26no—
309C4×C59—22no—
310C4×C59—22no—
311C4×C59—43no—
312C4×C59—43no—
313C4×C59C2×C4×D4112yes—
314Dic59—26no—
315Dic59—26no—
316Dic59—22no—
317Dic59—26no—
318Dic59—43no—
319Dic59C2×C4×Q814yescomplemented
320Dic59D4×Q814yescomplemented
321C2×D4×Q8—591no—
322C22×C4×Q8—591no—
323C22×C4×Q8—591no—
324#2365—593no—
325#2360—593no—
326#2360—593no—
327Q8×C4⋊C4—591no—
328D4×C4⋊C4—593no—
329Q8×C22⋊C4—591no—
330Q8×C22⋊C4D5911yescharacteristic, complemented
331C4×C4⋊Q8—593no—
332C4×C22⋊Q8—593no—
333C4×C22⋊Q8—593no—
334C42×Q8—591no—
335C42×D4—593no—
336C2×C59—24no—
337C2×C59C22×C4×D411yescharacteristic
338C2×C59C22×C4×Q811yescharacteristic
339C2×C59C4×2−1+411yescharacteristic
340C2×C59C2×D4×Q811yescharacteristic
341C2×C59D4×#4111yescharacteristic
342C2×C59Q8×#4111yescharacteristic
343C2×C59#348211yescharacteristic
344D59—24no—
345C23×Q8—591no—
346C23×Q8C2×D5911yescharacteristic
347D4×Q8—5916no—
348C2×C4⋊Q8—593no—
349C2×C22⋊Q8—593no—
350C2×C22⋊Q8—593no—
351C2×C4×Q8—591no—
352C2×C4×Q8—591no—
353C2×C4×Q8—593no—
354C2×C4×Q8—591no—
355C2×C4×Q8—593no—
356C2×C4×Q8—593no—
357C2×C4×Q8—593no—
358C2×C4×Q8—1188no—
359C2×C4×Q8—1188no—
360C2×C4×Q8C2×D5911yescharacteristic
361C2×C4×Q8C2×D5911yescharacteristic
362C2×C4×D4—593no—
363C2×C4×D4—591no—
364C2×C4×D4—593no—
365C22×C4⋊C4—593no—
366C22×C4⋊C4—593no—
367C22×C42—593no—
368C22×C42—593no—
369#391—593no—
370#391—593no—
371#391C2×D5913yes—
372#391C2×D5913yes—
373#389—593no—
374#389—593no—
375#389—596no—
376#389—596no—
377#387—596no—
378#387—596no—
379#385—596no—
380#385—596no—
381#384—593no—
382#380—593no—
383#380C2×D5913yes—
384C4×C4⋊C4—593no—
385C4×C4⋊C4—593no—
386C4×C4⋊C4—593no—
387C4×C4⋊C4—593no—
388C4×C4⋊C4—593no—
389C4×C4⋊C4—596no—
390C4×C4⋊C4—593no—
391C4×C22⋊C4—593no—
392C4×C22⋊C4—593no—
393C4×C22⋊C4—593no—
394C4×C22⋊C4—593no—
395C4×C22⋊C4—593no—
396C4×C22⋊C4C2×D5913yes—
397C43—593no—
398C59C4×D4×Q811yescharacteristic, complemented, Sylow
399C22×Q8—24no—
400C22×Q8—24no—
401C22×Q8—598no—
402C22×Q8—593no—
403C22×Q8—1184no—
404C22×Q8—1184no—
405C22×Q8C4×D5918yescomplemented
406C22×Q8C22×D5913yes—
407C22×Q8C22×D5911yescharacteristic
408C22×D4—591no—
409C23×C4—591no—
410C23×C4—593no—
411C23×C4—591no—
412C23×C4—593no—
413C23×C4—593no—
414C23×C4C22×D5913yes—
415C4⋊Q8—5924no—
416C22⋊Q8—5924no—
417C22⋊Q8—5924no—
418C4×Q8—24no—
419C4×Q8—24no—
420C4×Q8—598no—
421C4×Q8—598no—
422C4×Q8—11812no—
423C4×Q8—11812no—
424C4×Q8—11812no—
425C4×Q8—11812no—
426C4×Q8—1184no—
427C4×D4—5924no—
428C4×D4—598no—
429C4×D4—11812no—
430C2×C4⋊C4—593no—
431C2×C4⋊C4—593no—
432C2×C4⋊C4—591no—
433C2×C4⋊C4—593no—
434C2×C4⋊C4—596no—
435C2×C4⋊C4—593no—
436C2×C4⋊C4—596no—
437C2×C4⋊C4—596no—
438C2×C4⋊C4—593no—
439C2×C4⋊C4—596no—
440C2×C4⋊C4—11812no—
441C2×C4⋊C4—11812no—
442C2×C4⋊C4C22×D5913yes—
443C2×C4⋊C4C22×D5913yes—
444C2×C22⋊C4—593no—
445C2×C22⋊C4—593no—
446C2×C22⋊C4—591no—
447C2×C22⋊C4—593no—
448C2×C22⋊C4C22×D5913yes—
449C2×C22⋊C4C22×D5911yescharacteristic
450C2×C42—593no—
451C2×C42—591no—
452C2×C42—593no—
453C2×C42—593no—
454C2×C42—593no—
455C2×C42—593no—
456C2×C42—593no—
457C2×C42—593no—
458C2×C42—593no—
459C2×C42—593no—
460C2×C42—593no—
461C2×C42—11812no—
462C2×C42—11812no—
463C2×C42C22×D5913yes—
464C2×C42C22×D5913yes—
465#95—593no—
466#95—593no—
467#95—593no—
468#95—593no—
469#95—596no—
470#95—596no—
471#95C22×D5913yes—
472#95C22×D5913yes—
473#95C22×D5916yes—
474C24—591no—
475C24C23×D5911yescharacteristic
476C2×Q8—232no—
477C2×Q8—26no—
478C2×Q8—26no—
479C2×Q8—5912no—
480C2×Q8—11832no—
481C2×Q8—1186no—
482C2×Q8—1186no—
483C2×Q8C2×C4×D59112yes—
484C2×Q8C2×C4×D5914yes—
485C2×Q8D4×D5914yes—
486C2×Q8#1174568714yes—
487C2×D4—594no—
488C2×D4—594no—
489C2×D4—594no—
490C22×C4—26no—
491C22×C4—26no—
492C22×C4—591no—
493C22×C4—591no—
494C22×C4—594no—
495C22×C4—591no—
496C22×C4—593no—
497C22×C4—593no—
498C22×C4—593no—
499C22×C4—5912no—
500C22×C4—594no—
501C22×C4—593no—
502C22×C4—1182no—
503C22×C4—1182no—
504C22×C4—1186no—
505C22×C4—1186no—
506C22×C4—1182no—
507C22×C4—1182no—
508C22×C4—1186no—
509C22×C4—1186no—
510C22×C4—1186no—
511C22×C4—1186no—
512C22×C4—2363no—
513C22×C4—2363no—
514C22×C4C2×C4×D59112yes—
515C22×C4C23×D5913yes—
516C22×C4C23×D5913yes—
517C22×C4C23×D5913yes—
518C22×C4C23×D5911yescharacteristic
519C22×C4C23×D5911yescharacteristic
520C22×C4C23×D5913yes—
521C4⋊C4—26no—
522C4⋊C4—26no—
523C4⋊C4—5912no—
524C4⋊C4—5912no—
525C4⋊C4—5924no—
526C4⋊C4—5912no—
527C4⋊C4—594no—
528C4⋊C4—11812no—
529C4⋊C4—11812no—
530C4⋊C4—1186no—
531C4⋊C4—1186no—
532C4⋊C4—2366no—
533C22⋊C4—26no—
534C22⋊C4—5912no—
535C22⋊C4—5912no—
536C22⋊C4—594no—
537C22⋊C4—1186no—
538C22⋊C4Q8×D5914yescomplemented
539C42—26no—
540C42—26no—
541C42—5912no—
542C42—5912no—
543C42—594no—
544C42—1186no—
545C42—1186no—
546C42—1186no—
547C42—1186no—
548C42—1186no—
549C42—1186no—
550C42—1186no—
551C42—2363no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—592no—
557C23—592no—
558C23—592no—
559C23—1181no—
560C23—1181no—
561C23—1181no—
562C23—1181no—
563C23C22×C4×D5912yes—
564C23C2×Q8×D5912yes—
565C23#41×D5912yes—
566C23C24×D5911yescharacteristic
567Q8—224no—
568Q8—11824no—
569Q8(C22⋊D59)⋊C4116yesdirect product factor
570D4—5916no—
571C2×C4—21no—
572C2×C4—23no—
573C2×C4—21no—
574C2×C4—23no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—224no—
578C2×C4—23no—
579C2×C4—23no—
580C2×C4—23no—
581C2×C4—23no—
582C2×C4—23no—
583C2×C4—23no—
584C2×C4—592no—
585C2×C4—592no—
586C2×C4—592no—
587C2×C4—592no—
588C2×C4—592no—
589C2×C4—592no—
590C2×C4—596no—
591C2×C4—596no—
592C2×C4—596no—
593C2×C4—592no—
594C2×C4—1188no—
595C2×C4—1188no—
596C2×C4—1181no—
597C2×C4—1183no—
598C2×C4—1183no—
599C2×C4—1183no—
600C2×C4—1183no—
601C2×C4—1181no—
602C2×C4—1183no—
603C2×C4—1183no—
604C2×C4—11824no—
605C2×C4—1183no—
606C2×C4—1183no—
607C2×C4—1183no—
608C2×C4—23612no—
609C2×C4—23612no—
610C2×C4C22×C4×D5916yes—
611C2×C4C22×C4×D5916yes—
612C2×C4C2×D4×D5916yes—
613C2×C4C2×Q8×D5912yes—
614C2×C4C2×Q8×D5912yes—
615C2×C4C2×#1174568716yes—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22—594no—
623C22—1182no—
624C22—1182no—
625C22—1182no—
626C22—1182no—
627C22—1182no—
628C22—1182no—
629C22C4×Q8×D5914yescomplemented
630C22C23×C4×D5911yescharacteristic
631C22C22×D4×D5911yescharacteristic
632C22C22×Q8×D5911yescharacteristic
633C22C2×#41×D5911yescharacteristic
634C22C22×#1174568711yescharacteristic
635C222−1+4×D5911yescharacteristic
636C22#1683823911yescharacteristic
637C4—26no—
638C4—22no—
639C4—22no—
640C4—43no—
641C4—43no—
642C4—594no—
643C4—594no—
644C4—1186no—
645C4—1186no—
646C4—1182no—
647C4—1186no—
648C4—2363no—
649C4C2×(C22⋊D59)⋊C4112yes—
650C2—24no—
651C2—1184no—
652C2C22×(C22⋊D59)⋊C411yescharacteristic
653C2C2×C4×Q8×D5911yescharacteristic
654C2#2143730511yescharacteristic
655C2D4×Q8×D5911yescharacteristic
656C2#2143758511yescharacteristic
657C2Q8×#1174568711yescharacteristic
658C2#2143771211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D59
commutatorC22×C59C24×C4
FittingQ8×C22⋊C4×C59C2
socle, cosocleC23×C59C25
prime radicalC22×C22⋊D59C23
hypercenterQ8×C22⋊C4D59
hypocenterC59C4×D4×Q8
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ Q8×C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22×Q8×Dic59C2semidirect
3. C2×C4×Q8×D59C2semidirect
4. #21427153C2semidirect
5. #21427106C2semidirect
6. #21427099C2semidirect
7. Q8×Dic59⋊C4C2semidirect
9. Q8×(C2×D59)⋊C4C2semidirect
10. #21426665C2semidirect
11. #21426634C2semidirect
12. #21426624C2semidirect
13. C4×Q8×Dic59C2semidirect
15. Q8×C22⋊C4×C59C2semidirect
17. Q8×C22⋊D59C4semidirect
72. C2×Q8×D59C2×C4semidirect
79. #14273725C2×C4semidirect
80. #14273706C2×C4semidirect
81. #14273703C2×C4semidirect
85. Q8×Dic59C2×C4semidirect
86. Q8×Dic59D4semidirect
91. (C22⋊D59)⋊C4Q8direct (N × H)
129. C22×Q8×C59C2×C4semidirect
170. C22×Dic59C2×Q8semidirect
187. C2×C4×D59C2×Q8semidirect
194. C22⋊C4×C59C2×Q8semidirect
200. (C2×D59)⋊C4C2×Q8semidirect
210. Dic59⋊C4C2×Q8semidirect
221. C4×Dic59C2×Q8semidirect
238. Q8×C59C4×D4semidirect
258. C22⋊D59C4×Q8semidirect
293. C22×C59C2×C4×Q8semidirect
307. C2×D59C2×C4×Q8semidirect
319. Dic59C2×C4×Q8semidirect
320. Dic59D4×Q8semidirect
330. Q8×C22⋊C4D59semidirect
398. C59C4×D4×Q8semidirect
405. C22×Q8C4×D59semidirect
538. C22⋊C4Q8×D59semidirect
569. Q8(C22⋊D59)⋊C4direct (N × H)
629. C22C4×Q8×D59semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×Q8×C22⋊D592
C22×Q8×Dic592
C2×C4×Q8×D592
#214271532
#214271062
#214270992
Q8×Dic59⋊C42
#214269922
Q8×(C2×D59)⋊C42
#214266652
#214266342
#214266242
C4×Q8×Dic592
C4×(C22⋊D59)⋊C42
Q8×C22⋊C4×C592
C4×D4×Q859